I'll add some comments about business valuation.
Say I've got a money-tree (like a goldmine with a certain reserve of gold) that pays out $100 every year for 10 years. How much would you pay for it? Well, the lifetime revenue is $1000. But you wouldn't pay $1000, because of the time value of money. $100 in 1900 is worth only $2 today due to inflation of prices, for example. When you have $100 today and accrue interest for 10 years, it's worth a lot more than getting $100 in 10 years. So there's some 'discount rate' every year, so the money-tree might only be worth say $750. The rate depends on many factors, it's just an example.
This is roughly how companies are valued. You look at revenue streams and discount them over some time and then pay for that, minus some risk factor that the company fails. In addition, you may pay for various assets, but sometimes they can be a small factor. After all, assets are only valuable to generate revenue which you already calculate, or to sell. But some assets aren't very valuable when sold. (e.g. if Bitpay or bitcoin fails, its bitcoin payment processing software or its bitcoins will have little resale value. So for Bitpay, revenues are the big factor).
So let's look at Bitpay, they've recently stated in a developer presentation that they process about 1-2m a day. Say 500m a year. They also made public they grow at about 10% a month, which is equal to Coinbase, Blockchain.info and Multibit for example, so it's a very reasonable number. We can also say they take 1% as fees like Coinbase does.
So their revenues are 5m annually, today, and their growth rate is 3x annually. So for the next 5 years that's 5m, 15m, 45m, 135m, 405m.
See now where the 160m valuation comes from? Of course, this is a very rough calculation. For example, they make less than 1% in fees to be exact, it's probably closer to 0.75%. Their 3x growth per year is of course impossible to continue indefinitely, it may slow to 2x or even 1.5x at some point. And I haven't applied the discount rate yet (which isn't huge, by the way), nor the risk that bitcoin fails. (but then, it is *venture* capital). If you value a company on its 10-year revenue stream like is often done, 160m is a very realistic rate.
Now, let's be clear, Bitpay didn't make this valuation by itself. You've got a number of silicon valley / entrepreneurial legends turned investors (top-ranking ones) who offered to buy close to 20% for 30m. THAT is the valuation. These VCs made the valuation. Now you can say it's ridiculous without any arguments, but if I'd have to guess, I'd probably side with the VCs. They're self-made. Not by a single stroke of luck, but by series of successful companies and successful investments. You can be assured they've done their homework.
I'm not versed in how all this VC funding works, but is it possible for an entity to state that they're funding $X, but in reality are not, hoping/knowing that a true source with deep pockets will come along, saying to themselves, "If that entity is in for $X, I'm in for $Y."? Thus, now there's real money, namely $Y, to use for operating, development, pool parties naked by the hot tub, etc. And, not just $Y, but other venture capitalist don't want to be left out of making bank, so they, too, join the flock pumping in $Zs.